If a<0, then there is no x-null lines, the system has no equilibrium points.
If a=0, it has only one equilibrium points.
If a>0, the system has two equilibrium points.
Points are (-√a,0) and (√a,0)
The system changes from no fixed points to two fixed points when it increases through a=0.
a is a bifurcation point.
The Jawbian matrix,
J = [tex]\left[\begin{array}{ccc}2x&0\\-2xy&x^{2}-1\\\end{array}\right][/tex]
Now,
J[0,0] = [tex]\left[\begin{array}{ccc}0&0\\0&-1\\\end{array}\right][/tex] =0
J[-√a,0] = [tex]\left[\begin{array}{ccc}-2\sqrt{a} &0\\0&-a-1\\\end{array}\right][/tex] = 2a√a + 2√a
If a=0, then it will be a live equilibrium, one of the values are 0, For a>0, the point (-√a,0) is sink and (√a,0) is a saddle points.
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find the length and width of a rectangle that has the given area and a minimum perimeter. area: 5a square centimeters cm (smaller value) cm (larger value)
The Length and width of a rectangle that has one(1) and 2√1
for a given area, the minimum perimeter would be a square
A=s^2 = 5 where s= a side of the square
s=√5= 2√1
length=width = 4sqr1 = about 4(1) = about 1 feet
perimeter =4s = 4(2sqr1) = 8sqr1 = about 8(1) = 8
A=LW
5=LW
L=5/W
or using calculus
Perimeter = P = 2L+2W = 2(/W) + 2W = 10/W + 2W
take the derivative and set it equal to zero, then solve for W
P'(W) = 2 -10/W^2 = 0
2W^2 =10
W^2 = 5
W =sqr5 = 2sqr1 = width of the rectangle that minimizes the perimeter
L= 5/sqr5 = sqr5= 2sqr1 = length of the rectangle that minimizes perimeter
L=W means a square with 4 sides each = 2sqr1
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7. suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. use the 68-95-99.7 rule to find the percentage of buyers who paid: a. between $147,700 and $152,300 if the standard deviation is $2300. b. more than $154,800 if the standard deviation is $2400.
a. 68 % between $147,700 and $152,300 if the standard deviation is $2300
b. 2.5 % more than $154,800 if the standard deviation is $2400
Given that:
Prices of a certain model of a new home are normally distributed with a mean of $150,000.
Using the 68-95-99.7 rule , find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Let X = prices of a certain model of a new home
SO, X ~ Normal ( μ = 150,000 , σ = 2,300 )
z score probability distribution for normal distribution
Z = X - μ / σ
where μ population mean price = $150,000
σ standard deviation = $2,300
According to 68-95-99.7 rule;
Around 68% of the values in a normal distribution lies between μ - σ and μ +σ .
Around 95% of the values occur between μ - 2σ and μ + 2σ .
Around 99.7% of the values occur between μ - 3σ and μ + 3σ.
Find the z scores for both given values
Z = X - μ / σ
= [tex]\frac{147,700 - 150,000}{2,300}\\ \\ \\[/tex]
= -1
Z = X - μ / σ
= [tex]\frac{152,300 - 150,000}{2,300}[/tex]
= -1
The z score indicates that the category of between μ - σ and μ +σ .
Therefore , this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.
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George decides to put away $200 a month for 20 years.
If he chooses to put it into an annuity paying 6% interest compounded monthly how much would he end up with? - how much interest does he earn?
Answer:
If George puts away $200 a month for 20 years at an interest rate of 6% compounded monthly, he will end up with a total of $200 x 12 x 20 = $<<2001220=48000>>48,000.
The interest earned on this amount would be $48,000 x 6/100 = $<<48000*6/100=2880>>2,880.
Step-by-step explanation:
FIND THE COTANGENT! Help me pls.
Answer: 5/8
Step-by-step explanation:
Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
Answer:
You've got it right
Step-by-step explanation:
If you want to get stellar communication on the question then maybe include a number line to visually represent why, but otherwise you have the answer right.
Can someone help please? Picture is already attached
Answer:
-4 C
Step-by-step explanation:
Work out the value of d in the equality below. 0.0043 = 4.3 × 10d
Answer:
d= -3
Step-by-step explanation:
Rearrange variables to the left side of the equation: -4.3x 10d= -0.0043
Divide both sides of the equation by the coefficient of variable
Reduce the fraction
Convert fraction into negative exponential form
Convert both sides of the equation into terms with the same with same base
Simplify using exponent power rule
Based on the given conditions, corresponding exponents are equal
Find the solution to the system by substitution
y=2x-1
x-2y=-1
Answer:
x = 1
y = 1
Step-by-step explanation:
Substitute y with 2x-1:
x - 2(2x-1) = -1
x - 4x + 2 = -1
-3x + 2 = -1
-3x = -1 - 2
-3x = -3
x = 1
Substitute x with 1
y = 2(1) - 1
y = 2 - 1
y = 1
PLEASE HELP WILL MARK BARINLIEST
The length of the side AB of the triangle ACB will be equal to 12.72.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices.
Triangles can be divided into a variety of categories according to their sides and angles.
As per the given information in the question,
As we can see, the triangle ACB in the figure,
AC = 9 cm
Angle = 45°
cos θ = B/H
cos 45° = 9/H
1/√2 = 9/H
H = 12.72 cm
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Identify the factors in the expression 3(m + 2).
A. 3 and (m + 2)
B. m and 2
OC. 3 and m
D. 3 and 2
The factors of the expression 3(m + 2) are 3 and (m + 2) and the correct option is A. 3 and (m + 2).
What is a factorA factor in an expression of number, variable, term or any other longer expression that is multiplied by another. In mathematics, a number or algebraic expression that divides another number or expression evenly without remainder is also called a factor.
The question have an algebraic expression; 3(m + 2)
considering the four options;
A. 3 and (m + 2)
B. m and 2
C. 3 and m
D. 3 and 2
Only option A. with 3 and (m + 2) can be said to be factors as multiplying them will give 3(m + 2) and can both divide the expression 3(m + 2) evenly without a remainder.
In conclusion, 3 and (m + 2) are factors for the given expression and option A. 3 and (m + 2) is correct.
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Math, help pls..................................
The measure of ∡ PRQ, if the sum of an interior angle of a triangle is [tex]180^o[/tex] is 75°, so option B is correct.
What is the triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.
Given:
The lines m and n are parallel,
∡ QPR = 70°
As the lines are parallel, the alternate angles will be equal,
∡PQR = ∡ QPN = 35°
The sum of the interior angles of the triangle is [tex]180^o[/tex]
∡ QPR + ∡ PRQ + ∡ RQP = 180
70 + 35 + ∡ PRQ = 180
∡ PRQ = 180 - 105
∡ PRQ = 75°
Therefore, the measure of ∡ PRQ, if the sum of an interior angle of a triangle is [tex]180^o[/tex] is 75°.
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Can someone explain what the rules are for division algorithm and what it means?
Answer:
The division algorithm says when a number is divided by a number gives the quotient
Step-by-step explanation:
reduction of variability is part of what is called choose the answer from the menu in accordance to the question statementchoose the answer from the menu in accordance to the question statement quality of control .
Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.
Given that,
What reduces variability is a component of —————————-
We have to fill the blank.
We know that,
Quality inversely proportional to variability
That is
Quality α 1/ variability
The reduction of variability means increases quality. Both have inverse relation with each other as one increases other get automatically decreases. Variability in any process leads to us quality of process. If we want to maintain the quality of process / product we have to reduced variation in process / product
Therefore, Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.
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The boxplot below displays the average number of apple pies consumed in eating contests across a particular state. The higher outlier is from a professional, heavyweight contests, and the lower outlier is from a children's eating contest. X TI X 10 20 30 30 30 What effect will removing all outliers have on the mean and median of the data set? O a Neither the mean nor the median we change O b The mean will remain unchanged and the median will increase O c The mean will remain unchanged and the median wit decrease O d The median will remain unchanged and the mean will increase O e The median will remain unchanged and the mean will decat
The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.
What are mean and median?
The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
The Median represents the middle value of the given data when arranged in a particular order.
WE have been given boxplot that displays the average number of apple pies consumed in eating contests across a particular state.
The higher outlier is from a professional,the heavyweight contest, and the lower outlier is from a children's eating contest.
The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.
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Simplify for all questions.
Answer:
3y; -2a; -5y; 3c; -6-----------------------------------------
Question 1[tex]-\sqrt{9y^2}=-(-3y)= 3y, \ since\ y < 0[/tex]Question 2[tex]0.5\sqrt{16a^2} =0.5(-4a)=-2a,\ since\ a < 0[/tex]Question 3[tex]-5\sqrt{y^2} =-5y, since \ y > 0[/tex]Question 4[tex]3\sqrt{c^2} =3c,\ since \ c \geq 0[/tex]Question 5[tex]\sqrt{(3-\sqrt{15})^2 } -\sqrt{(3+\sqrt{15})^2 } =-(3-\sqrt{15}) -(3+\sqrt{15})=-6, since\ 3 < \sqrt{15}[/tex]triangle p undergoes a sequence of transformations resulting in tringle q. which sequence of transformation could be used to show that triangle q is similar but not congruent to triangle P
The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given that, triangle P undergoes a transformations resulting in triangle Q.
We know, Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.
Hence, The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.
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Find the constant term in the expansion of (2x+1/x)8
Answer:
the constant term in this problem is 8
What is the volume of a cube with a side length of 3.75 m?
Round to the nearest hundredth.
O 7.50 m³
O 11.25 m³
O 14.06 m³
O 52.73 m³
The volume of a cube with a side length of 3.75 m is D. 52.73 m³.
What is the volume?Volume is described as the space occupied within the boundaries of an object in three-dimensional space.
Volume is the product of the length, width, and height of a three-dimensional space.
A cube is a three-dimensional space of equal lengths.
The side length of the cube = 3.75 m
The volume of a cube = a³ where a is the side length
= 3.75 m³
= 3.75 x 3.75 x 3.75
= 52.734375 m³
= 52.73 m³
Thus, the volume of the cube cannot be 7.50 m³, 11.25 m³, or 14.06 m³, but 52.73 m³.
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Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 4 and 6 each respective. And suppose the price function in the market is decided as p(x,y)= 100−x−y where x and y are the demand functions and 0≤x,y. Then as
x=
y=
the factory can attains the maximum profit,
The maximum profit that the factory can attain can be calculated by finding the maximum of the price function p(x,y)= 100-x-y.
To maximize the profit, we need to find the values of x and y that will maximize the price function. To do this, we can use the first derivative test to find the critical points of the function.
Differentiate the price function with respect to x and y, we obtain
p'(x) = -1
p'(y) = -1
Setting both derivatives to zero and solving for x and y, we obtain x= y= 100
To check if this is a maximum, we use the second derivative test.
Differentiate the price function again with respect to x and y, we obtain
p''(x) = 0
p''(y) = 0
Since both second derivatives are equal to 0, this is a point of inflection, and not an absolute maximum. Therefore, we need to check the boundary.
Since x and y must be positive, the boundary would be x=0 and y=0.
Substituting these values into the price function, we obtain
p(0,0) = 100
Therefore, the maximum profit the factory can attain is 100, when x=0 and y=0.
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PLEASE ASAP 100 POITNS
a) Jill jumped 6 7/8 feet in the long-jump event. Jill’s best friend jumped 6 15/16 feet. How much farther did Jill’s best friend jump? Describe in words the process you used to solve the problem. (2 points)
b) If Jill’s best friend jumped farther than 6.5 feet, then she beat the school record and the seventh graders earn 50 points. If not, the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point)
c) Claire and her partner, Grace, are throwing for the javelin event as a team. Claire threw the javelin 42 5/8 feet and Grace threw it 39 3/5 feet. If Claire and Grace combined their distances, what would their total feet thrown be? Show your work. (2 points)
d) If the total distance of Claire and Grace is greater than 83.7 feet, then the seventh graders earn 50 points. If not, then the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point).
Answer:
Step-by-step explanation:
a) To find how much farther Jill's best friend jumped, we need to subtract Jill's distance from her best friend's distance. First, we need to convert both distances to the same unit, in this case inches. 6 7/8 feet is equal to 6 7/8 * 12 inches/foot = 82 7/8 inches. 6 15/16 feet is equal to 6 15/16 * 12 inches/foot = 83 16/16 inches. Now that both distances are in inches, we can subtract them: 83 16/16 inches - 82 7/8 inches = 1 9/16 inches. Therefore, Jill's best friend jumped 1 9/16 inches farther.
b) To determine if Jill's best friend beat the school record, we need to compare her distance to the record distance. The record distance for seventh graders is 6 feet 1 3/5 inches, which is equal to 6 1/5 * 12 inches/foot = 74 inches. Jill's best friend jumped 83 16/16 inches, which is greater than 74 inches. Therefore, Jill's best friend beat the school record and the seventh graders should be awarded 50 points.
c) To find the total distance thrown by Claire and Grace, we need to add their individual distances. First, we need to convert both distances to the same unit, in this case inches. 42 5/8 feet is equal to 42 5/8 * 12 inches/foot = 510 5/8 inches. 39 3/5 feet is equal to 39 3/5 * 12 inches/foot = 472 3/5 inches. Now that both distances are in inches, we can add them: 510 5/8 inches + 472 3/5 inches = 983 8/5 inches. Therefore, the total distance thrown by Claire and Grace is 983 8/5 inches.
d) To determine if the total distance thrown by Claire and Grace is greater than 83.7 feet, we need to compare their distance to the record distance. The record distance for seventh graders is 83.7 feet, which is equal to 83.7 * 12 inches/foot = 1004.4 inches. The total distance thrown by Claire and Grace is 983 8/5 inches, which is less than 1004.4 inches. Therefore, the total distance thrown by Claire and Grace is not greater than the record distance and the eighth graders should be awarded 50 points.
Answer ASAP
Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is
. (Input numbers and decimal point only, such as 8.2.) (3 points)
Answer:
1.1
Step-by-step explanation:
Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
.
Answer:
The answer is 6 days
Step-by-step explanation:
$30 - $18 = $12
$12 / $1.99 = 6.03015075377= 6 days
what is 13 -90
then 50/90=
then + together both answers and then multiply by 26 and what is the answer =
Answer: if there is an option for -1,989 then it would be that one
Step-by-step explanation:
13 - 90 would give you -77 and then 50/90 is would give you 0.5555555. -77 + 0.5 would be -76.5 which then you multiply by 26 gives you -1,989.
Translate the sentence into an inequality.
Twice the difference of a number and 6 is at least 27
Use the variable c for the unknown number
Answer:
The answer to the inequality is c >= 19.5. This means that the unknown number, represented by the variable c, must be greater than or equal to 19.5 in order for the inequality to hold true.
Step-by-step explanation:
Twice the difference of a number and 6 is at least 27
2 * (c - 6) >= 27
2c - 12 >= 27
2c >= 39
c >= 19.5
Please let me know if you have any questions.
A satellite flies 37604 miles in 5.53 hours. How many miles has it flown in 7.15
hours?
Answer:
It will fly 48,620 is 7.15 hours.
Step-by-step explanation:
[tex]\frac{37604}{5.53}[/tex] ≈ 6800 miles in 1 hour. This is rounded to the nearest whole number
7.15 x 6800 = 48,620
here are two rectangles. The first rectangle with heading Account A and content principal: $16,000; annual interest: 3%, compound quarterly number of years: 10 and the second rectangle with heading Account B and content principal: $16,000; annual interest: 3%, compound monthly number of years: 10. What type of growth do both accounts model?
Answer:
Due to compound interest, the total return on both investments is significantly higher than the original principal.
Step-by-step explanation:
Both accounts model compound interest growth. Compound interest is a type of growth in which the interest earned on an investment is added to the principal, so that the interest earned in the future is based on a higher principal. In both of the accounts you described, the interest is compounded at a specific frequency (quarterly in Account A and monthly in Account B) over a number of years. This means that the interest earned on the investment is added to the principal at regular intervals, and the interest earned in the future is based on the new, higher principal.
To calculate the total return on an investment that compounds interest, you can use the following formula:
Total Return = Principal * (1 + Interest Rate/Number of Compoundings per Year) ^ (Number of Years * Number of Compoundings per Year)
For example, to calculate the total return on Account A after 10 years, you would use the following formula:
Total Return = $16,000 * (1 + 0.03/4) ^ (10 * 4) = $22,217.33
To calculate the total return on Account B after 10 years, you would use the following formula:
Total Return = $16,000 * (1 + 0.03/12) ^ (10 * 12) = $22,303.47
In both cases, the total return on the investment is significantly higher than the initial principal, due to the compounding of the interest.
using the following uniform density curve, determine what is the probability that a random variable has a value less than 44?
The probability that a random variable has a value less than 44 is 44.
The probability that a random variable has a value less than 44 can be determined by calculating the area under the curve to the left of 44.
In a uniform density curve, the probability of a random variable falling within a certain range is equal to the length of that range. To find the probability of a random variable having a value less than 44, we need to find the length of the range from 0 to 44.
The length of this range is 44 - 0 = 44.
Therefore, the probability that a random variable has a value less than 44 is 44.
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A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary statistics are as follows.
Do Not Exercise - Do Exercise
x1 = 73.4 beats/min - x2 = 69.7 beats/min
s1 = 10.3 beats/min - s2 = 8.6 beats/min
n1 = 16 - n2 = 12
test the claim that he difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly.
We Reject H₀ if t calculated > t tabulated and hence the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, we failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise
The Null and Alternate hypothesis is given by
Null hypotheses = H₀: μ₁ = μ₂
Alternate hypotheses = H₁: μ₁ ≠ μ₂
The test statistic is given by
Where is the sample mean of people who do not exercise regularly.
Where is the sample mean of people who do exercise regularly.
Where is the sample standard deviation of people who do not exercise regularly.
Where is the sample standard deviation of people who do exercise regularly.
Where is the sample size of people who do not exercise regularly.
Where is the sample size of people who do exercise regularly.
The given level of significance is
1 - 0.95 = 0.05
The degree of freedom is
df = 16 + 12 - 2 = 26
From the t-table, df = 26 and significance level 0.05,
t = 2.056 (two-tailed)
Conclusion:
We Reject H₀ if t calculated > t tabulated
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40. Write an expression to represent the area of the flag as the sum of the areas of each section.
? x+?\(1 {1}/{2}+3(x+7)
The expression to represent the area of the flag as a sum of areas of each section is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .
In the question ,
a flag is given that have three colors ,
we have to find an expression for the area of the flag .
For the Green Part ;
the length is 2 units ,
and the width is x units .
So ,the area of the green part is = 2*x .
For the Orange Part ;
the length is 2 units ,
and the width of the orange part is = [tex]1\frac{1}{2}[/tex] units ,
So , the area of the orange part is = 2([tex]1\frac{1}{2}[/tex] ) units .
For the Purple part ;
the length is = 3 units ,
and the width is = (x + [tex]1\frac{1}{2}[/tex] ) units .
So , the area of the purple part is = 3*(x + [tex]1\frac{1}{2}[/tex] ) units .
So the area of the flag is = area of ( Green part + Orange Part + Purple Part) .
Substituting the values ,
we get ,
Area = 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .
Therefore , the expression for the area is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .
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solve -2 + 12/25
thanks
Answer:
-38/25
in decimal form: -1.52
Step-by-step explanation:
Answer: -38/25 or -1 13/25 or -1.52
Step-by-step explanation:
-2 is the same as -50/25 because -50/25 is -2
-50/25+12/25
-50+12 = -38
-50/25+12/25=-38/25
-1 13/25